Question: Solve for $r$, $ \dfrac{2}{25r} = \dfrac{3}{15r} + \dfrac{2r + 8}{5r} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $25r$ $15r$ and $5r$ The common denominator is $75r$ To get $75r$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{2}{25r} \times \dfrac{3}{3} = \dfrac{6}{75r} $ To get $75r$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{3}{15r} \times \dfrac{5}{5} = \dfrac{15}{75r} $ To get $75r$ in the denominator of the third term, multiply it by $\frac{15}{15}$ $ \dfrac{2r + 8}{5r} \times \dfrac{15}{15} = \dfrac{30r + 120}{75r} $ This give us: $ \dfrac{6}{75r} = \dfrac{15}{75r} + \dfrac{30r + 120}{75r} $ If we multiply both sides of the equation by $75r$ , we get: $ 6 = 15 + 30r + 120$ $ 6 = 30r + 135$ $ -129 = 30r $ $ r = -\dfrac{43}{10}$